Study On The Growth Characteristics Of Fatigue Cracks In The Tooth Root Based On Peridynamic

Tooth root cracking fatigue failure is one of the common forms of gear failure.As a means of understanding crack expansion behaviour and estimating crack expansion life,numerical simulation of tooth root fatigue crack expansion has important engineering applications.Current studies of this type,mostly finite element based,often face problems of crack tip region singularities and complex crack front mesh regeneration during implementation.Peridynamic theory uses equations of motion based on the integral form of displacement instead of the differential form in traditional mechanical theory,which can effectively avoid the singularity problem that exists when using traditional mechanical models to deal with fatigue crack tip problems;under the peridynamic model,damage fracture belongs to the force state vector,and crack sprouting and expansion occur naturally without additional criteria or the need for finite element The crack emergence and expansion is natural and does not require additional criteria,nor does it require regeneration of the material points at the crack front as in the finite element model.The computational efficiency and applicability of fatigue crack extension simulation analysis can be improved.In this paper,a numerical simulation model of fatigue crack expansion is developed based on peridynamic and the expansion characteristics of fatigue cracks in tooth roots are investigated,with the main contents including:Firstly,a brief overview of the peridynamic contact theory,peridynamic fracture theory,and the Peridigm ildftware,which can implement the peridynamic algorithm,is provided.The simulations of simple contact cases are then carried out using the established peridynamic contact model,and the results are compared with the results of the finite element method to ensure the peridynamic contact model’s accuracy.Secondly,using the peridynamic fracture model,we simulate the crack-expansion process of a flat plate with various starting crack types under a certain load and investigate the impact of various beginning crack forms on the flat plate’s crack-expansion path.The length,angle,and placement of the initial crack are the primary concerns of this work.After extrapolating the stress intensity factor based on nodal displacement,the stress intensity factor at the tip of the flat fracture is computed.The resulting stress intensity factor is then compared to the theoretically predicted value.Finally,a quasi-static analysis of the gear meshing process based on the peridynamic method is carried out to determine the maximum bending stress point at the tooth root during the meshing process of a healthy gear,and this point is used as the crack initiation point;after the initial crack is prefabricated,the damage module of the gear is defined in the script file,the critical elongation is determined according to its material intrinsic structure relationship,and the crack expansion path is obtained by running the script file;based on this crack Based on this crack extension path,a certain amount of crack extension is taken under the original initial crack model to further delineate the crack,while the stress intensity factor at the crack tip is calculated using the nodal displacement-based stress intensity factor extrapolation method;the stress intensity factor is then combined with the Paris formula to calculate the tooth root fatigue crack extension life.